Regardless, if learning is to be as efficient and deep as possible, it’s essential that it be done freely. That means giving children a voice in which activities to participate, for how long, and also the level of mastery they want to achieve. (“This is the biggest clash with traditional curriculum development,” Droujkova notes.)
— Vangelova (2014): 5-Year-Olds Can Learn Calculus
This article provides a lot of evidence to support the notion that the conceptual aspects of calculus and other “higher level” forms of math should be taught at all age levels, not just at the end of high school or in college.
Flint switches from Detroit’s water system to the Flint River to save money,
E. coli bacteria show up in water (E.coli can make you sick) so the water system adds chlorine to kill the bacteria,
Trichloromethane shows up in the water (trichloromethane is a carcinogen)
Water from the Flint River is more corrosive compared to Detroit’s because it has higher levels of chlorine ions (Cl–),
Chlorine dissolves lead from old water pipes — the lead goes into solution in the water (lead causes issues with mental development in kids, among other things),
KCL: Current flow into a node must equal the flow out of the node. (A node is a point on the wire connecting components in a circuit–usually a junction).
(KCL: Kirchoff’s Current Law) Current flowing into any point on a circuit is equal to the current flowing out of it, A simple circuit with a voltage source (like a battery) and a resistor.
KVC: The sum of all the voltage differences in a closed loop is zero.
KVL: The voltage difference across the battery (9 Volts) plus the voltage difference across the resistor (-9 Volts) is equal to zero.
Things get more interesting when we get away from simple circuits.
Current flow into a node (10 A) equals the flow out of the node (7 A + 3 A).
Note that the convention for drawing diagrams is that the current move from positive (+) to negative (-) terminals in a battery. This is opposite the actual flow of electrons in a typical wired circuit because the current is a measure of the movement of negatively charged electrons, but is used for historical reasons.
The Siege of Miami: A detailed report that looks at the increasing frequency of flooding in Miami, because of sea-level-rise. The reporter interviews a number of scientists and engineers who are not terribly optimistic about the long-term (50+ years) future of many Floridian cities because of the melting ice-caps in Greenland and Antarctica.
Flooded street during a “King Tide” in Miami Beach, Florida. Image from NOAA.
The last sub-atomic particle discovered was the Higgs boson, which is shown in the graph below.
Finding the Higgs Boson “The strongest evidence for this new particle comes from analysis of events containing two photons. The smooth dotted line traces the measured background from known processes. The solid line traces a statistical fit to the signal plus background. The new particle appears as the excess around 126.5 GeV. The full analysis concludes that the probability of such a peak is three chances in a million. ” from ATLAS.
A quick program that animates scaling (dilation) of shapes by scaling the coordinates. You type in the dilation factor.
dilation.py
from visual import *
#axes
xmin = -10.
xmax = 10.
ymin = -10.
ymax = 10.
xaxis = curve(pos=[(xmin,0),(xmax,0)])
yaxis = curve(pos=[(0,ymin),(0,ymax)])
#tick marks
tic_dx = 1.0
tic_h = .5
for i in arange(xmin,xmax+tic_dx,tic_dx):
tic = curve(pos=[(i,-0.5*tic_h),(i,0.5*tic_h)])
for i in arange(ymin,ymax+tic_dx,tic_dx):
tic = curve(pos=[(-0.5*tic_h,i),(0.5*tic_h,i)])
#stop scene from zooming out too far when the curve is drawn
scene.autoscale = False
# define curve here
shape = curve(pos=[(-1,2), (5,3), (4,-1), (-1,-1)])
shape.append(pos=shape.pos[0])
shape.color = color.yellow
shape.radius = 0.1
shape.visible = True
#dilated shape
dshape = curve(color=color.green, radius=shape.radius*0.9)
for i in shape.pos:
dshape.append(pos=i)
#label
note = label(pos=(5,-8),text="Dilation: 1.0", box=False)
intext = label(pos=(5,-9),text="> x", box=False)
#scaling lines
l_scaling = False
slines = []
for i in range(len(shape.pos)):
slines.append(curve(radius=shape.radius*.5,color=color.red, pos=[shape.pos[i],shape.pos[i],shape.pos[i]]))
#animation parameters
animation_time = 1. #seconds
animation_smootheness = 30
animation_rate = animation_smootheness / animation_time
x = ""
while 1:
#x = raw_input("Enter Dilation: ")
if scene.kb.keys: # event waiting to be processed?
s = scene.kb.getkey() # get keyboard info
#print s
if s <> '\n':
x += s
intext.text = "> x "+x
else:
try:
xfloat = float(x)
note.text = "Dilation: " + x
endpoints = []
dp = []
for i in shape.pos:
endpoints.append(float(x) * i)
dp.append((endpoints[-1]-i)/animation_smootheness)
#print "endpoints: ", endpoints
#print "dp: ", dp
for i in range(animation_smootheness):
for j in range(len(dshape.pos)):
dshape.pos[j] = i*dp[j]+shape.pos[j]
rate(animation_smootheness)
if slines:
for i in range(len(shape.pos)):
slines[i].pos[1] = vector(0,0)
slines[i].pos[-1] = dshape.pos[i]
for i in range(len(shape.pos)):
dshape.pos[i] = endpoints[i]
slines[i].pos[-1] = dshape.pos[i]
for i in range(len(shape.pos)-1):
print shape.pos[i], "--->", dshape.pos[i]
except:
#print "FAIL"
failed = True
intext.text = "> x "
x = ""
